Subgroups — C₇₉×#25717 #34137406

Order 20224.

2234 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#127×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#492×C₇₉	C₂	1	2	yes	maximal, complemented
3	C₂×#450×C₇₉	C₂	1	4	yes	maximal, complemented
4	C₇₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2014	C₂	1	4	yes	maximal, complemented
6	C₇₉×#1957	C₂	1	2	yes	maximal, complemented
7	C₄×C₂²⋊C₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₇₉	—	2	2	no	—
9	C₂³×D₄×C₇₉	C₂²	1	2	yes	—
10	C₂²×SD₁₆×C₇₉	C₂²	1	8	yes	complemented
11	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
12	C₂×#127×C₇₉	—	2	8	no	—
13	C₂×#127×C₇₉	—	2	2	no	—
14	C₂×#127×C₇₉	C₂²	1	2	yes	—
15	C₂×#127×C₇₉	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
18	#492×C₇₉	—	2	8	no	—
19	#450×C₇₉	—	2	16	no	—
20	C₂×#102×C₇₉	C₂²	1	8	yes	complemented
21	C₂×C₂²⋊C₈×C₇₉	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	complemented
23	#391×C₇₉	C₂²	1	2	yes	complemented
24	#389×C₇₉	—	2	2	no	—
25	#384×C₇₉	C₂²	1	1	yes	characteristic, complemented
26	#380×C₇₉	—	2	2	no	—
27	#336×C₇₉	C₂²	1	2	yes	complemented
28	C₂⁵×C₇₉	—	2	2	no	—
29	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
30	C₂²×D₄×C₇₉	—	2	16	no	—
31	C₂²×D₄×C₇₉	—	2	8	no	—
32	C₂²×D₄×C₇₉	—	2	2	no	—
33	C₂²×D₄×C₇₉	—	2	4	no	—
34	C₂²×D₄×C₇₉	—	2	4	no	—
35	C₂²×D₄×C₇₉	—	2	8	no	—
36	C₂²×D₄×C₇₉	—	4	4	no	—
37	C₂²×D₄×C₇₉	—	4	8	no	—
38	C₂²×D₄×C₇₉	—	4	8	no	—
39	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
40	C₂³×C₄×C₇₉	D₄	1	2	yes	—
41	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
42	C₂×SD₁₆×C₇₉	—	2	16	no	—
43	C₂×SD₁₆×C₇₉	—	2	16	no	—
44	C₂×SD₁₆×C₇₉	—	4	8	no	—
45	C₂²×C₈×C₇₉	C₂³	1	4	yes	—
46	C₄⋊Q₈×C₇₉	—	2	4	no	—
47	#127×C₇₉	—	2	16	no	—
48	#127×C₇₉	—	2	8	no	—
49	#127×C₇₉	—	2	4	no	—
50	#127×C₇₉	D₄	1	8	yes	—
51	C₂²⋊Q₈×C₇₉	—	2	8	no	—
52	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
56	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
57	C₂×C₄²×C₇₉	—	2	4	no	—
58	C₂×C₄²×C₇₉	D₄	1	2	yes	—
59	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
61	#102×C₇₉	—	2	16	no	—
62	C₂²⋊C₈×C₇₉	D₄	1	8	yes	complemented
63	C₄×C₈×C₇₉	—	2	4	no	—
64	#95×C₇₉	—	2	4	no	—
65	C₂⁴×C₇₉	—	2	8	no	—
66	C₂⁴×C₇₉	—	2	4	no	—
67	C₂⁴×C₇₉	—	4	4	no	—
68	C₂⁴×C₇₉	—	4	8	no	—
69	C₂⁴×C₇₉	—	4	4	no	—
70	C₂⁴×C₇₉	—	4	8	no	—
71	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
72	C₂×Q₈×C₇₉	—	2	4	no	—
73	C₂×Q₈×C₇₉	—	2	4	no	—
74	C₂×Q₈×C₇₉	—	2	4	no	—
75	C₂×D₄×C₇₉	—	2	8	no	—
76	C₂×D₄×C₇₉	—	2	16	no	—
77	C₂×D₄×C₇₉	—	2	16	no	—
78	C₂×D₄×C₇₉	—	2	8	no	—
79	C₂×D₄×C₇₉	—	2	4	no	—
80	C₂×D₄×C₇₉	—	2	8	no	—
81	C₂×D₄×C₇₉	—	4	32	no	—
82	C₂×D₄×C₇₉	—	4	4	no	—
83	C₂×D₄×C₇₉	—	4	8	no	—
84	C₂×D₄×C₇₉	—	4	64	no	—
85	C₂×D₄×C₇₉	—	4	4	no	—
86	C₂×D₄×C₇₉	—	4	8	no	—
87	C₂×D₄×C₇₉	—	4	8	no	—
88	C₂×D₄×C₇₉	—	4	8	no	—
89	C₂×D₄×C₇₉	C₂×D₄	1	8	yes	—
90	C₂²×C₄×C₇₉	—	2	4	no	—
91	C₂²×C₄×C₇₉	—	2	4	no	—
92	C₂²×C₄×C₇₉	—	2	2	no	—
93	C₂²×C₄×C₇₉	—	2	2	no	—
94	C₂²×C₄×C₇₉	—	2	2	no	—
95	C₂²×C₄×C₇₉	—	2	2	no	—
96	C₂²×C₄×C₇₉	SD₁₆	1	8	yes	complemented
97	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
102	SD₁₆×C₇₉	—	4	32	no	—
103	C₂×C₈×C₇₉	—	2	4	no	—
104	C₂×C₈×C₇₉	—	2	4	no	—
105	C₂×C₈×C₇₉	C₂×D₄	1	8	yes	complemented
106	C₄⋊C₄×C₇₉	—	2	4	no	—
107	C₄⋊C₄×C₇₉	—	4	4	no	—
108	C₄⋊C₄×C₇₉	—	4	4	no	—
109	C₄⋊C₄×C₇₉	—	4	4	no	—
110	C₂²⋊C₄×C₇₉	—	4	4	no	—
111	C₄²×C₇₉	—	2	4	no	—
112	C₄²×C₇₉	—	2	2	no	—
113	C₄²×C₇₉	C₂×D₄	1	4	yes	—
114	C₂³×C₇₉	—	2	1	no	—
115	C₂³×C₇₉	—	2	1	no	—
116	C₂³×C₇₉	—	2	2	no	—
117	C₂³×C₇₉	—	2	8	no	—
118	C₂³×C₇₉	—	4	16	no	—
119	C₂³×C₇₉	—	4	32	no	—
120	C₂³×C₇₉	—	4	4	no	—
121	C₂³×C₇₉	—	4	4	no	—
122	C₂³×C₇₉	—	4	8	no	—
123	C₂³×C₇₉	—	4	8	no	—
124	C₂³×C₇₉	—	8	8	no	—
125	C₂³×C₇₉	—	8	16	no	—
126	C₂³×C₇₉	—	8	8	no	—
127	C₂³×C₇₉	#127	1	2	yes	—
128	C₂³×C₇₉	C₂×SD₁₆	1	4	yes	—
129	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
130	Q₈×C₇₉	—	4	8	no	—
131	D₄×C₇₉	—	2	16	no	—
132	D₄×C₇₉	—	4	16	no	—
133	D₄×C₇₉	—	4	32	no	—
134	D₄×C₇₉	—	4	8	no	—
135	D₄×C₇₉	—	4	32	no	—
136	C₂×C₄×C₇₉	—	2	1	no	—
137	C₂×C₄×C₇₉	—	2	2	no	—
138	C₂×C₄×C₇₉	—	2	1	no	—
139	C₂×C₄×C₇₉	—	2	2	no	—
140	C₂×C₄×C₇₉	—	2	8	no	—
141	C₂×C₄×C₇₉	—	2	16	no	—
142	C₂×C₄×C₇₉	—	4	2	no	—
143	C₂×C₄×C₇₉	—	4	2	no	—
144	C₂×C₄×C₇₉	—	4	2	no	—
145	C₂×C₄×C₇₉	—	4	2	no	—
146	C₂×C₄×C₇₉	—	4	4	no	—
147	C₂×C₄×C₇₉	#120	1	4	yes	—
148	C₂×C₄×C₇₉	#127	1	2	yes	—
149	C₂×C₄×C₇₉	C₂×SD₁₆	1	4	yes	—
150	C₂×C₄×C₇₉	C₂×SD₁₆	1	4	yes	—
151	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	4	yes	—
152	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
153	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
154	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
155	C₈×C₇₉	—	2	8	no	—
156	C₂²×C₇₉	—	2	2	no	—
157	C₂²×C₇₉	—	2	2	no	—
158	C₂²×C₇₉	—	2	4	no	—
159	C₂²×C₇₉	—	2	4	no	—
160	C₂²×C₇₉	—	4	8	no	—
161	C₂²×C₇₉	—	4	16	no	—
162	C₂²×C₇₉	—	8	32	no	—
163	C₂²×C₇₉	—	8	4	no	—
164	C₂²×C₇₉	—	8	4	no	—
165	C₂²×C₇₉	—	8	8	no	—
166	C₂²×C₇₉	#492	1	4	yes	complemented
167	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
168	C₂²×C₇₉	C₂×#127	1	1	yes	characteristic
169	C₂²×C₇₉	#535	1	1	yes	characteristic
170	C₂²×C₇₉	C₂²×SD₁₆	1	2	yes	—
171	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
172	C₄×C₇₉	—	2	2	no	—
173	C₄×C₇₉	—	2	4	no	—
174	C₄×C₇₉	—	8	2	no	—
175	C₄×C₇₉	—	8	2	no	—
176	C₄×C₇₉	#450	1	8	yes	complemented
177	C₄×C₇₉	D₄²	1	4	yes	—
178	#25717	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂×C₇₉	—	2	4	no	—
180	C₂×C₇₉	—	8	8	no	—
181	C₂×C₇₉	#2433	1	1	yes	characteristic
182	C₂×C₇₉	C₂×#450	1	2	yes	—
183	C₂×C₇₉	C₂×#492	1	1	yes	characteristic
184	C₂×C₇₉	#3151	1	1	yes	characteristic
185	C₂×C₇₉	#3208	1	2	yes	—
186	C₂²×#127	C₂×C₇₉	1	1	yes	characteristic
187	C₂×#492	C₂×C₇₉	1	2	yes	complemented
188	C₂×#450	C₂×C₇₉	1	4	yes	complemented
189	#2857	C₂×C₇₉	1	1	yes	characteristic, complemented
190	#2014	C₂×C₇₉	1	4	yes	complemented
191	#1957	C₂×C₇₉	1	2	yes	complemented
192	C₄×C₂²⋊C₈	C₂×C₇₉	1	1	yes	characteristic, complemented
193	C₇₉	#25717	1	1	yes	characteristic, direct product factor, Sylow
194	C₂³×D₄	—	2	2	no	—
195	C₂³×D₄	C₂²×C₇₉	1	2	yes	—
196	C₂²×SD₁₆	C₂²×C₇₉	1	8	yes	complemented
197	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
198	C₂×#127	—	2	8	no	—
199	C₂×#127	—	2	2	no	—
200	C₂×#127	C₂²×C₇₉	1	2	yes	—
201	C₂×#127	C₂²×C₇₉	1	2	yes	—
202	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	2	yes	—
203	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
204	#492	—	2	8	no	—
205	#450	—	2	16	no	—
206	C₂×#102	C₂²×C₇₉	1	8	yes	complemented
207	C₂×C₂²⋊C₈	C₂²×C₇₉	1	2	yes	—
208	C₂×C₄×C₈	C₂²×C₇₉	1	2	yes	complemented
209	#391	C₂²×C₇₉	1	2	yes	complemented
210	#389	—	2	2	no	—
211	#384	C₂²×C₇₉	1	1	yes	characteristic, complemented
212	#380	—	2	2	no	—
213	#336	C₂²×C₇₉	1	2	yes	complemented
214	C₂⁵	—	2	2	no	—
215	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
216	C₂²×D₄	—	2	16	no	—
217	C₂²×D₄	—	2	8	no	—
218	C₂²×D₄	—	2	2	no	—
219	C₂²×D₄	—	2	4	no	—
220	C₂²×D₄	—	2	4	no	—
221	C₂²×D₄	—	2	8	no	—
222	C₂²×D₄	—	4	4	no	—
223	C₂²×D₄	—	4	8	no	—
224	C₂²×D₄	—	4	8	no	—
225	C₂²×D₄	C₂³×C₇₉	1	4	yes	—
226	C₂³×C₄	D₄×C₇₉	1	2	yes	—
227	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
228	C₂×SD₁₆	—	2	16	no	—
229	C₂×SD₁₆	—	2	16	no	—
230	C₂×SD₁₆	—	4	8	no	—
231	C₂²×C₈	C₂³×C₇₉	1	4	yes	—
232	C₄⋊Q₈	—	2	4	no	—
233	#127	—	2	16	no	—
234	#127	—	2	8	no	—
235	#127	—	2	4	no	—
236	#127	D₄×C₇₉	1	8	yes	—
237	C₂²⋊Q₈	—	2	8	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
242	C₂×C₂²⋊C₄	—	2	2	no	—
243	C₂×C₄²	—	2	4	no	—
244	C₂×C₄²	D₄×C₇₉	1	2	yes	—
245	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
247	#102	—	2	16	no	—
248	C₂²⋊C₈	D₄×C₇₉	1	8	yes	complemented
249	C₄×C₈	—	2	4	no	—
250	#95	—	2	4	no	—
251	C₂⁴	—	2	8	no	—
252	C₂⁴	—	2	4	no	—
253	C₂⁴	—	4	4	no	—
254	C₂⁴	—	4	8	no	—
255	C₂⁴	—	4	4	no	—
256	C₂⁴	—	4	8	no	—
257	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	—	2	4	no	—
260	C₂×Q₈	—	2	4	no	—
261	C₂×D₄	—	2	8	no	—
262	C₂×D₄	—	2	16	no	—
263	C₂×D₄	—	2	16	no	—
264	C₂×D₄	—	2	8	no	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	—	2	8	no	—
267	C₂×D₄	—	4	32	no	—
268	C₂×D₄	—	4	4	no	—
269	C₂×D₄	—	4	8	no	—
270	C₂×D₄	—	4	64	no	—
271	C₂×D₄	—	4	4	no	—
272	C₂×D₄	—	4	8	no	—
273	C₂×D₄	—	4	8	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	C₂×D₄×C₇₉	1	8	yes	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	SD₁₆×C₇₉	1	8	yes	complemented
283	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₇₉	1	4	yes	—
285	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
287	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
288	SD₁₆	—	4	32	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	C₂×D₄×C₇₉	1	8	yes	complemented
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	4	4	no	—
294	C₄⋊C₄	—	4	4	no	—
295	C₄⋊C₄	—	4	4	no	—
296	C₂²⋊C₄	—	4	4	no	—
297	C₄²	—	2	4	no	—
298	C₄²	—	2	2	no	—
299	C₄²	C₂×D₄×C₇₉	1	4	yes	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	8	no	—
304	C₂³	—	4	16	no	—
305	C₂³	—	4	32	no	—
306	C₂³	—	4	4	no	—
307	C₂³	—	4	4	no	—
308	C₂³	—	4	8	no	—
309	C₂³	—	4	8	no	—
310	C₂³	—	8	8	no	—
311	C₂³	—	8	16	no	—
312	C₂³	—	8	8	no	—
313	C₂³	#127×C₇₉	1	2	yes	—
314	C₂³	C₂×SD₁₆×C₇₉	1	4	yes	—
315	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
316	Q₈	—	4	8	no	—
317	D₄	—	2	16	no	—
318	D₄	—	4	16	no	—
319	D₄	—	4	32	no	—
320	D₄	—	4	32	no	—
321	D₄	—	4	8	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	16	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	#120×C₇₉	1	4	yes	—
334	C₂×C₄	#127×C₇₉	1	2	yes	—
335	C₂×C₄	C₂×SD₁₆×C₇₉	1	4	yes	—
336	C₂×C₄	C₂×SD₁₆×C₇₉	1	4	yes	—
337	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	4	yes	—
338	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
339	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
340	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
341	C₈	—	2	8	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	4	8	no	—
347	C₂²	—	4	16	no	—
348	C₂²	—	8	32	no	—
349	C₂²	—	8	4	no	—
350	C₂²	—	8	4	no	—
351	C₂²	—	8	8	no	—
352	C₂²	#492×C₇₉	1	4	yes	complemented
353	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
354	C₂²	C₂×#127×C₇₉	1	1	yes	characteristic
355	C₂²	#535×C₇₉	1	1	yes	characteristic
356	C₂²	C₂²×SD₁₆×C₇₉	1	2	yes	—
357	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	2	yes	—
358	C₄	—	2	2	no	—
359	C₄	—	2	4	no	—
360	C₄	—	8	2	no	—
361	C₄	—	8	2	no	—
362	C₄	#450×C₇₉	1	8	yes	complemented
363	C₄	D₄²×C₇₉	1	4	yes	—
364	C₂	—	2	4	no	—
365	C₂	—	8	8	no	—
366	C₂	C₇₉×#2433	1	1	yes	characteristic
367	C₂	C₂×#450×C₇₉	1	2	yes	—
368	C₂	C₂×#492×C₇₉	1	1	yes	characteristic
369	C₂	C₇₉×#3151	1	1	yes	characteristic
370	C₂	C₇₉×#3208	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂²×#127×C₇₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂²×C₄²×C₇₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×#492×C₇₉	C₂	semidirect
3. C₂×#450×C₇₉	C₂	semidirect
4. C₇₉×#2857	C₂	semidirect
5. C₇₉×#2014	C₂	semidirect
6. C₇₉×#1957	C₂	semidirect
7. C₄×C₂²⋊C₈×C₇₉	C₂	semidirect
10. C₂²×SD₁₆×C₇₉	C₂²	semidirect
11. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
20. C₂×#102×C₇₉	C₂²	semidirect
22. C₂×C₄×C₈×C₇₉	C₂²	semidirect
23. #391×C₇₉	C₂²	semidirect
25. #384×C₇₉	C₂²	semidirect
27. #336×C₇₉	C₂²	semidirect
62. C₂²⋊C₈×C₇₉	D₄	semidirect
96. C₂²×C₄×C₇₉	SD₁₆	semidirect
105. C₂×C₈×C₇₉	C₂×D₄	semidirect
166. C₂²×C₇₉	#492	semidirect
176. C₄×C₇₉	#450	semidirect
178. #25717	C₇₉	direct (N × H)
187. C₂×#492	C₂×C₇₉	semidirect
188. C₂×#450	C₂×C₇₉	semidirect
189. #2857	C₂×C₇₉	semidirect
190. #2014	C₂×C₇₉	semidirect
191. #1957	C₂×C₇₉	semidirect
192. C₄×C₂²⋊C₈	C₂×C₇₉	semidirect
193. C₇₉	#25717	direct (N × H)
196. C₂²×SD₁₆	C₂²×C₇₉	semidirect
197. C₂×C₄⋊Q₈	C₂²×C₇₉	semidirect
206. C₂×#102	C₂²×C₇₉	semidirect
208. C₂×C₄×C₈	C₂²×C₇₉	semidirect
209. #391	C₂²×C₇₉	semidirect
211. #384	C₂²×C₇₉	semidirect
213. #336	C₂²×C₇₉	semidirect
248. C₂²⋊C₈	D₄×C₇₉	semidirect
282. C₂²×C₄	SD₁₆×C₇₉	semidirect
291. C₂×C₈	C₂×D₄×C₇₉	semidirect
352. C₂²	#492×C₇₉	semidirect
362. C₄	#450×C₇₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#127×C₇₉	2
C₂×#492×C₇₉	2
C₂×#450×C₇₉	2
C₇₉×#2857	2
C₇₉×#2014	2
C₇₉×#1957	2
C₄×C₂²⋊C₈×C₇₉	2
#25717	79

Subgroups — C79×#25717 #34137406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25717 #34137406